1.3 Argand Diagrams

    Cards (60)

    • An Argand diagram is a graphical representation of complex numbers on a two-dimensional plane
    • Complex numbers in the form a+a +bi bi are plotted with aa on the real axis and bb on the imaginary axis.
    • How would the complex number 3+3 +4i 4i be plotted on an Argand diagram?

      (3, 4)
    • Match the axis with its representation:
      Horizontal Axis ↔️ Real axis
      Vertical Axis ↔️ Imaginary axis
    • Steps to plot a complex number on an Argand diagram:
      1️⃣ Identify the real part
      2️⃣ Identify the imaginary part
      3️⃣ Plot the point (a, b) on the plane
    • The real axis on an Argand diagram represents the imaginary part of a complex number.
      False
    • Where is the complex number 2+2 +3i 3i plotted on an Argand diagram?

      (2, 3)
    • What is an Argand Diagram used for?
      Representing complex numbers
    • In an Argand Diagram, the real part of a complex number is plotted on the horizontal
    • The imaginary axis in an Argand Diagram corresponds to the y-axis in a Cartesian Plane.
    • What is the vertical axis in an Argand Diagram called?
      Imaginary axis
    • Match the components of an Argand Diagram with their counterparts in a Cartesian Plane:
      Horizontal Axis ↔️ x-axis
      Vertical Axis ↔️ y-axis
    • Where is the complex number 3+3 +4i 4i plotted on an Argand Diagram?

      (3, 4)
    • To plot a complex number on an Argand Diagram, you must identify its real and imaginary parts.
    • Steps to plot a complex number on an Argand Diagram:
      1️⃣ Identify the real and imaginary parts.
      2️⃣ Locate the point on the diagram.
      3️⃣ Mark the point to represent the complex number.
    • The real axis in an Argand Diagram is horizontal.
    • What are the two axes in an Argand Diagram called?
      Real and imaginary axes
    • In an Argand Diagram, complex numbers are plotted using their real and imaginary parts.
    • What are the axes of an Argand Diagram called?
      Real and imaginary axes
    • The imaginary axis in an Argand Diagram is vertical
    • Match the diagram type with its axis names:
      Argand Diagram ↔️ Real axis ||| Imaginary axis
      Cartesian Plane ↔️ x-axis ||| y-axis
    • The complex number 3+3 +4i 4i is plotted as (3, 4) on an Argand Diagram.
    • How do you plot a complex number a+a +bi bi on an Argand Diagram?

      Locate point (a, b)
    • The modulus of a complex number z = a + bi</latex> is its distance from the origin
    • The formula for the modulus of z=z =a+ a +bi bi is z=|z| = \sqrt{a^{2} + b^{2}}.
    • What does the modulus of a complex number represent graphically?
      Distance from the origin
    • The modulus of a complex number is always a positive real number.
    • The argument of a complex number z=z =a+ a +bi bi is the angle θ\theta calculated as \theta = \tan^{ - 1}\left(\frac{b}{a}\right)</latex>.origin
    • What is the argument of z=z =3+ 3 +4i 4i in terms of tan1\tan^{ - 1}?

      tan1(43)\tan^{ - 1}\left(\frac{4}{3}\right)
    • The argument of a complex number is measured from the positive real axis.
    • What is the argument of z=z =3+ 3 +4i 4i?

      tan1(43)\tan^{ - 1}\left(\frac{4}{3}\right)
    • What is the argument of a complex number defined as?
      The angle θ\theta between the positive real axis and the line connecting the origin to zz on an Argand Diagram
    • The argument of a complex number z = a + bi</latex> is calculated as θ=\theta =tan1(ba) \tan^{ - 1}\left(\frac{b}{a}\right)
    • On which diagram is the argument of a complex number represented graphically?
      Argand Diagram
    • For z=z =3+ 3 +4i 4i, the argument is θ=\theta =tan1(43) \tan^{ - 1}\left(\frac{4}{3}\right), which is the angle in radians
    • What does the calculation of the argument of a complex number depend on?
      The quadrant of zz
    • In the first quadrant, if a>0a > 0 and b>0b > 0, then θ=\theta =tan1(ba) \tan^{ - 1}\left(\frac{b}{a}\right)
    • What is the formula for θ\theta in the second quadrant when a<0a < 0 and b>0b > 0?

      θ=\theta =π+ \pi +tan1(ba) \tan^{ - 1}\left(\frac{b}{a}\right)
    • What is the argument of a complex number defined as?
      Angle between positive real axis and z
    • The argument for z=z =3+ 3 +4i 4i is calculated as tan1(43)\tan^{ - 1}\left(\frac{4}{3}\right), which simplifies to \theta
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